[math-fun] Prof.Dr. Landau's polynomial decomposition
I suppose you could call a poly "prime" if it has no such decomposition. (And I use the term literally: "de-composition.") New kind of primeness notion. Seems to me Macsyma et al ought to offer finding this decomposition as yet another capability. Could be useful. If Landau does it over finite fields then doing it over integers (and perhaps rationals?) could be done via some kind of chinese remaindering of finite field results. In a finite field, there is a problem however. Some polynomial decomposition F(x)=G(H(x)) could happen, even though H and/or G actually have greater degree than F. Right? Can Landau detect those? Doubt it. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
Jean-Charles Faugère & Ludovic Perret An efficient algorithm for decomposing multivariate polynomials and its applications to cryptography, Journal of Symbolic Computation Volume 44 Issue 12, December, 2009 Pages 1676-1689 generalizes the Kozen-Landau decomposition algorithm to multivariate polynomials (or so it claims). I took a brief look at the original Kozen-Landau JSC paper and it seems very good. Oddly enough, Landau is now a professor of "social policy" which is not the subject you might have expected. I saw her testifying to congress about the FBI/Apple case, I thought she was doing great; but unfortunately far as I know nothing she did affected the US government's brain-dead conceptions about crypto & the law. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
Date: Sun, 3 Apr 2016 21:40:53 -0400 From: Warren D Smith <warren.wds@gmail.com>
Oddly enough, Landau is now a professor of "social policy" which is not the subject you might have expected. I saw her testifying to congress about the FBI/Apple case, I thought she was doing great; but unfortunately far as I know nothing she did affected the US government's brain-dead conceptions about crypto & the law.
Her testimony is widely cited by policy makers and may well influence policy going forward. It's a big government, it contains multitudes. Hilarie
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Warren D Smith